1. Executive Summary

This report analyzes 7 participants performing Fitts’ law pointing tasks across two input modalities (Hand, Gaze) and two UI modes (Static, Adaptive).

Key Findings

Total Trials Analyzed: 1306 valid trials (correct responses, RT 150-6000ms)
Total Trials Collected: 1485
Overall Error Rate: 12%
Mean Throughput: 2.91 bits/s (SD = 0.74)
Mean Movement Time: 1.277s (SD = 0.516s)

2. Demographics

Overall Demographics

N	Mean Age	SD Age	Age Range	Mean Gaming (Hrs/Week)	SD Gaming
7	28	8.8	18 - 42	0.9	1.2

By Gender

gender	Count	Avg Age	SD Age	Avg Gaming (Hrs)
female	1	28	NA	0
male	6	28	9.6	1

Input Device Distribution

input_device	Count	Percentage
mouse	7	100

3. Primary Analysis: Throughput

Research Question: Does the Adaptive UI improve performance (Throughput) compared to Static, especially for Gaze?

Summary Statistics

Throughput (bits/s) by Condition
modality	ui_mode	pressure	N	Mean	SD	Median	Q25	Q75
hand	static	1	21	3.16	0.69	3.22	2.72	3.60
hand	adaptive	1	21	3.19	0.73	3.22	2.57	3.81
gaze	static	1	21	2.72	0.61	2.72	2.38	3.03
gaze	adaptive	1	21	2.57	0.74	2.52	2.02	3.10

Visualizations

Throughput by Modality and UI Mode. Higher values indicate better performance. White diamonds show mean values. Violin plots show the distribution shape, boxplots show quartiles, and individual points may be visible as outliers.

Statistical Model Results

⚠ **Statistical model could not be fitted for Throughput.**

**Reason:**  Model fitting failed: contrasts can be applied only to factors with 2 or more levels 

**Diagnostics:**
- Participants:  7 
- Total trials:  84 
- Conditions:  4 
- Minimum trials per condition:  21 
- Empty conditions:  0 

**Trials per condition:**
# A tibble: 4 × 4
  modality ui_mode  pressure     n
  <fct>    <fct>    <fct>    <int>
1 hand     static   1           21
2 hand     adaptive 1           21
3 gaze     static   1           21
4 gaze     adaptive 1           21

4. Movement Time Analysis

Research Question: How does movement time vary across conditions?

Summary Statistics

Movement Time (s) by Condition
modality	ui_mode	pressure	N	Mean	SD	Median
hand	static	1	358	1.195	0.391	1.119
hand	adaptive	1	362	1.160	0.296	1.110
gaze	static	1	285	1.334	0.501	1.215
gaze	adaptive	1	301	1.460	0.757	1.212

Visualizations

Movement Time by Modality and UI Mode. Lower values indicate faster performance. White diamonds show mean values. Violin plots show the distribution shape, boxplots show quartiles, and individual points may be visible as outliers.

Statistical Model Results

⚠ **Statistical model could not be fitted for Movement Time.**

**Reason:**  Model fitting failed: contrasts can be applied only to factors with 2 or more levels 

**Diagnostics:**
- Participants:  7 
- Total trials:  1306 
- Conditions:  4 
- Minimum trials per condition:  285 
- Empty conditions:  0 

**Trials per condition:**
# A tibble: 4 × 4
  modality ui_mode  pressure     n
  <fct>    <fct>    <fct>    <int>
1 hand     static   1          358
2 hand     adaptive 1          362
3 gaze     static   1          285
4 gaze     adaptive 1          301

5. Fitts’ Law Modelling

Research Question: How well does the data fit Fitts’ Law? (Linearity check). Flatter slopes indicate less sensitivity to difficulty (ballistic movement).

Fitts’ Law Regression (Movement Time vs Effective Index of Difficulty). The effective index of difficulty (IDe) is calculated using the effective target width (We) derived from the spatial distribution of selection endpoints. Shaded regions around regression lines represent 95% confidence intervals. Linear regression fits are shown separately for each modality and UI mode combination.


### Model Fit Statistics

Linear Regression: MT ~ IDe
modality	ui_mode	r_squared	slope	intercept
hand	static	0.709	0.190	0.464
hand	adaptive	0.820	0.154	0.576
gaze	static	0.617	0.240	0.468
gaze	adaptive	0.464	0.357	0.198

6. Error Rate Analysis

Research Question: How do error rates differ across conditions?

Error Rates by Condition
modality	ui_mode	pressure	Total	Errors	Error_Rate
hand	static	1	378	20	5.29
hand	adaptive	1	378	16	4.23
gaze	static	1	351	66	18.80
gaze	adaptive	1	378	77	20.37

Error Rate by Modality and UI Mode. Lower values indicate fewer errors. Error rate is calculated as the percentage of trials with incorrect selections (misses, timeouts, or false activations). White diamonds show mean values. Violin plots show the distribution shape, boxplots show quartiles.

Statistical Model Results

⚠ **Statistical model could not be fitted for Error Rate.**

**Reason:**  Model fitting failed: contrasts can be applied only to factors with 2 or more levels 

**Diagnostics:**
- Participants:  7 
- Total trials:  1485 
- Conditions:  4 
- Minimum trials per condition:  351 
- Empty conditions:  0 
- Overall error rate:  12.1 %

**Trials per condition:**
# A tibble: 4 × 4
  modality ui_mode  pressure     n
  <fct>    <fct>    <fct>    <int>
1 hand     static   1          378
2 hand     adaptive 1          378
3 gaze     static   1          351
4 gaze     adaptive 1          378

7. Accuracy & Gaze Dynamics

Effective Width (\(W_e\))

Lower \(W_e\) indicates tighter shot grouping (higher precision).

Effective Width (px) by Condition
modality	ui_mode	pressure	Mean_We	SD_We
hand	static	1	34.07	20.05
hand	adaptive	1	35.47	22.51
gaze	static	1	36.91	18.32
gaze	adaptive	1	37.80	17.75

Effective Target Width (Accuracy) by Modality and UI Mode. Lower values indicate tighter shot grouping and higher precision. Effective width (We) is calculated as 4.133 × SD of projected errors along the task axis, normalizing to a 4% error rate. White diamonds show mean values. Violin plots show the distribution shape, boxplots show quartiles.

Endpoint Accuracy Scatter Plot

Visualization of endpoint errors relative to target center. Each point represents one trial’s endpoint position.

Endpoint Error Distance (px) for Gaze Modality
ui_mode	pressure	N	Mean_Error	SD_Error	Median_Error
static	1	285	12.29	8.09	10.41
adaptive	1	301	12.48	7.98	10.88

The “Midas Touch” Struggle

Target Re-entries measure how often the cursor drifted out of the target before selection.

Target Re-entries by Condition
modality	ui_mode	pressure	Mean_Reentries	SD_Reentries
hand	static	1	0.00	0.00
hand	adaptive	1	0.00	0.00
gaze	static	1	1.99	0.91
gaze	adaptive	1	2.11	0.91

Target Re-entries (Control Stability) by Modality and UI Mode. Re-entries count how often the cursor drifted out of the target before final selection, measuring control stability during the verification phase. Counts > 1 indicate slipping out of target. Lower values are better. White diamonds show mean values. Violin plots show the distribution shape, boxplots show quartiles.

8. Workload (NASA-TLX)

Subjective workload scores (lower is better).

NASA-TLX Workload Scores by Modality and UI Mode. Scores range from 0-100, where lower values indicate lower subjective workload. The six TLX scales (Mental Demand, Physical Demand, Temporal Demand, Performance, Effort, Frustration) are shown separately. White diamonds show mean values. Violin plots show the distribution shape, boxplots show quartiles.

Overall NASA-TLX Workload Score. Average across all 6 scales (Mental, Physical, Temporal, Performance, Effort, Frustration). Lower values indicate lower overall subjective workload. White diamonds show mean values. Violin plots show the distribution shape, boxplots show quartiles.

NASA-TLX Workload Components (Stacked Bar Chart). Total height represents overall workload, with each colored segment representing one of the six TLX scales (Mental Demand, Physical Demand, Temporal Demand, Performance, Effort, Frustration). Lower total height indicates lower overall subjective workload.

9. Learning Curves & Practice Effects

Research Question: How does performance change within each condition? Do learning rates differ by condition?

This section shows learning curves aligned by condition start (accounting for Williams counterbalancing). For block-level trends, see Section 12.

Learning Curve Data Summary by Condition
Modality	UI Mode	Pressure	N Positions	Mean RT (s)	Mean Error Rate
Hand	Static	ON	27	1.194	0.0529
Hand	Adaptive	ON	27	1.161	0.0423
Gaze	Static	ON	27	1.330	0.1880
Gaze	Adaptive	ON	27	1.462	0.2037

Learning Curves: Movement Time Within Condition. Learning aligned by position within condition (accounting for counterbalancing). LOESS smoothing. Lower is better. Shaded regions show 95% CI.

Error Rate Summary by Condition
Modality	UI Mode	Pressure	N Positions	Mean Error Rate	Min Error Rate	Max Error Rate
Hand	Static	ON	27	5.29%	0.00%	14.29%
Hand	Adaptive	ON	27	4.23%	0.00%	14.29%
Gaze	Static	ON	27	18.80%	0.00%	46.15%
Gaze	Adaptive	ON	27	20.37%	7.14%	42.86%

Learning Curves: Error Rate Within Condition. Learning aligned by position within condition (accounting for counterbalancing). LOESS smoothing. Lower is better. Shaded regions show 95% CI.

Note: Data aligned by position within condition to account for Williams counterbalancing. For block-level trends, see Section 12: Block Order & Temporal Effects.

10. Movement Quality Metrics

Submovement Analysis

Research Question: Does adaptive UI reduce movement corrections? How do submovements relate to performance?

Submovements indicate intermittent control - fewer submovements suggest smoother, more ballistic movements.

⚠ submovement_count column not found in dataset.

Verification Time Analysis

Research Question: How much time is spent “stopping” vs. “moving”? Does adaptive UI reduce verification time?

Verification time represents the “precise stopping” phase, separate from the ballistic movement phase.

11. Error Patterns & Types

Research Question: What types of errors occur? Do error patterns differ by condition?

Error Type Distribution by Condition
modality	ui_mode	pressure	err_type	Count	Total	Percentage
hand	static	1	miss	19	20	95.0
hand	static	1	timeout	1	20	5.0
hand	adaptive	1	miss	16	16	100.0
gaze	static	1	slip	66	66	100.0
gaze	adaptive	1	timeout	1	77	1.3
gaze	adaptive	1	slip	76	77	98.7

Error Type Distribution. Breakdown of error types by condition. Stacked bars show absolute counts for each error type (Miss, Timeout, Slip).

Error Type Proportions. Relative distribution of error types. Stacked bars show percentage of each error type (Miss, Timeout, Slip) within each condition.

12. Block Order & Temporal Effects

Research Question: Are there order effects? Does performance improve or degrade over blocks?

Performance Across Blocks: Throughput. Throughput by block number. Higher is better. Shaded regions show ±1 SE.

Block-Level Data Summary by Condition
Modality	UI Mode	Pressure	N Blocks	Mean Error Rate
Hand	Static	ON	6	5.56%
Hand	Adaptive	ON	6	4.28%
Gaze	Static	ON	5	19.44%
Gaze	Adaptive	ON	6	16.69%

Performance Across Blocks: Movement Time. Movement time by block number. Lower is better. Shaded regions show ±1 SE.

Performance Across Blocks: Error Rate. Error rate by block number. Lower is better. Shaded regions show ±1 SE.

13. Spatial Patterns & Heatmaps

Research Question: Are there spatial biases in performance? Do some screen regions show better/worse performance?

Performance by Target Position

Error Density Heatmap

Where do endpoint errors occur? Are there systematic spatial biases?

14. Adaptive UI Mechanism Analysis

Width Scaling (Target Size Adaptation)

Research Question: Does the adaptive UI dynamically change target sizes? How does width scaling relate to performance?

The adaptive UI may scale target widths based on performance. This section examines whether and how target sizes are adjusted.

⚠ Width scaling columns not found in dataset.

Alignment Gate Metrics

Research Question: If alignment gates are used, how do they affect performance? How often are false triggers detected?

Alignment gates may be used to ensure proper cursor alignment before selection. This section examines their usage and effectiveness.

⚠ Alignment gate columns not found in dataset.

Task Type Analysis

Research Question: Are there different task types (point vs. drag)? How does performance differ across task types?

If the experiment includes different task types, this section examines performance differences.

⚠ task_type column not found in dataset.

15. Gaze-Specific Analysis

Hover Time (Dwell Duration)

Research Question: How long do people hover before confirming? Does adaptive UI change dwell behavior?

For gaze modality, hover time represents the dwell duration before confirmation.

⚠ No valid hover time data available for gaze modality.

16. Summary & Conclusions

Key Findings Summary

Summary of Key Metrics by Condition
modality	ui_mode	Metric	Mean	SD
hand	static	Effective Width (px)	34.070	20.050
hand	adaptive	Effective Width (px)	35.470	22.510
gaze	static	Effective Width (px)	36.910	18.320
gaze	adaptive	Effective Width (px)	37.800	17.750
hand	static	Error Rate (%)	5.290	22.420
hand	adaptive	Error Rate (%)	4.230	20.160
gaze	static	Error Rate (%)	18.800	39.130
gaze	adaptive	Error Rate (%)	20.370	40.330
hand	static	Movement Time (s)	1.195	0.391
hand	adaptive	Movement Time (s)	1.160	0.296
gaze	static	Movement Time (s)	1.334	0.501
gaze	adaptive	Movement Time (s)	1.460	0.757
hand	static	Throughput (bits/s)	3.160	0.690
hand	adaptive	Throughput (bits/s)	3.190	0.730
gaze	static	Throughput (bits/s)	2.720	0.610
gaze	adaptive	Throughput (bits/s)	2.570	0.740

Data Quality Notes

Participants: 7
Valid Trials: 1306 (out of 1485 total experimental trials)
Exclusion Rate: 12% (due to errors, timeouts, or invalid RTs)
Trials per Participant: Mean = 186.6, Range = 164 - 209